Question

Madeline has an annuity that pays $7,902 at the beginning of a term twice a year. If the economy grows at a rate of 3.1% twice a year, what is the value of the annuity if she received it in a lump sum now rather than over a period of 16 years?

$198,170.44

$163,868.69

$201,242.08

$158,941.50

Answer 1

Someone help please??

Answer 2

I think you can solve this using
\[ \text{Future Value}= \text{payment}\cdot \frac{(1+i)^n-1}{i} \]
and
\[ \text{Future Value}= \text{Present Value}\cdot (1+i)^n\]
n is the number of periods, 2 times a year for 16 years, or n=32
economy grows at a rate of 3.1% twice a year, so i= 0.031 per 6 months
the payment is $7,902

Answer 3

Now find the future value, using the first equation.
use the future value in the second equation to find the present value, which is the answer to the question.